These are real algebraic curves inside the polytope \(P_{A,b}\) .
Following [1]},
we call \(\mathcal {C}^{R,+}_{A,b,c}\)  the central path of the linear program (REF ),
and we call \(\mathcal {C}^{T,+}_{A,b,c}\)  the entropic path of (REF ).
A slight distinction to [2]}, [1]} is that our central path
travels from the vertex of \(P_{A,b}\)  where \(c\)  is minimized to the vertex where
\(c\)  is maximized, passing through the analytic center of \(P_{A,b}\) .
For instance, Figure 1 in [1]} shows all real points on the central curve. The central
path is the piece inside the shaded hexagon \(P_{A,b}\) . That diagram
illustrates the transportation problem in Example REF .
